Renrong Mao

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All published works

Action	Title	Year	Authors
+ PDF Chat	Asymptotic formulas for the coefficients of the truncated theta series	2024	Renrong Mao
+ PDF Chat	Congruences modulo powers of $5$ for odd ranks	2024	Renrong Mao Zhiqian Zhou
+	Modular forms and congruences for k-marked odd Durfee symbols	2024	Renrong Mao
+	CONGRUENCES FOR RANKS OF PARTITIONS	2024	Renrong Mao
+	Andrews-Beck type congruences modulo powers of 5	2024	Nankun Hong Renrong Mao
+	A modular approach to Andrews-Beck partition statistics	2023	Renrong Mao
+ PDF Chat	A proof of a conjecture of Mao on Beck's partition statistics modulo 8	2023	Renrong Mao Ernest X. W. Xia
+	A proof of Mao’s conjecture on an identity of Beck’s partition statistics	2023	Renrong Mao Ernest X. W. Xia
+	Congruences for Andrews-Beck partition statistics modulo powers of primes	2023	Renrong Mao
+	Andrews-Beck type congrences modulo powers of 5	2023	Nankun Hong Renrong Mao
+	A proof of a conjecture of Mao on Beck's partition statistics modulo 8	2023	Renrong Mao Ernest X. W. Xia
+	Congruences for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">spt</mml:mi></mml:mrow><mml:mo>‾</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>ω</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> modulo powers of primes	2022	Renrong Mao
+	On total number parts functions associated to ranks of overpartitions	2021	Renrong Mao
+	On the total number of parts functions associated with ranks of partitions modulo 5 and 7	2021	Renrong Mao
+ PDF Chat	Variations of Andrews-Beck type congruences	2020	Song Heng Chan Renrong Mao Robert Osburn
+	ARITHMETIC PROPERTIES OF COEFFICIENTS OF THE MOCK THETA FUNCTION	2019	Renrong Mao
+	Two identities on the mock theta function V0(q)	2019	Renrong Mao
+	Inequalities between first moments of $$M_2$$-rank and crank for overpartitions	2019	Renrong Mao
+	On the non-negativity of the spt-crank for partitions without repeated odd parts	2018	Renrong Mao
+	Asymptotic formulas for spt-crank of partitions	2017	Renrong Mao
+	Inequalities Between Odd Moments of Rank and Crank for Overpartitions	2017	Renrong Mao
+	Some new expansions for certain truncated q-series	2017	Renrong Mao
+	Truncated series from the quintuple product identity	2016	Song Heng Chan Thi Phuong Nhi Ho Renrong Mao
+	Asymptotic formulas for M2-ranks of partitions without repeated odd parts	2016	Renrong Mao
+ PDF Chat	On recursions for coefficients of mock theta functions	2015	Song Heng Chan Renrong Mao Robert Osburn
+	The rank and crank of partitions modulo 3	2015	Song Heng Chan Renrong Mao
+	<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-rank of overpartitions and harmonic weak Maass forms	2015	Renrong Mao
+	Proofs of two conjectures on truncated series	2014	Renrong Mao
+	The $$M_{2}$$ M 2 -rank of partitions without repeated odd parts modulo $$6$$ 6 and $$10$$ 10	2014	Renrong Mao
+	Asymptotics for rank moments of overpartitions	2014	Renrong Mao
+	Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions	2014	Song Heng Chan Renrong Mao
+	Some new asymptotic expansions of certain partial theta functions	2013	Renrong Mao
+	Asymptotic inequalities for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math>-ranks and their cumulation functions	2013	Renrong Mao
+	Ranks of partitions modulo 10	2013	Renrong Mao
+	Inequalities between rank moments of overpartitions	2013	Renrong Mao
+	On ranks of partitions and congruences of special functions	2013	Renrong Mao
+	Pairs of partitions without repeated odd parts	2012	Song Heng Chan Renrong Mao
+	TWO CONGRUENCES FOR APPELL–LERCH SUMS	2011	Song Heng Chan Renrong Mao

Common Coauthors

Coauthor	Papers Together
Song Heng Chan	7
Ernest X. W. Xia	3
Nankun Hong	2
Robert Osburn	2
Thi Phuong Nhi Ho	1
Zhiqian Zhou	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Some Properties of Partitions	1954	A. O. L. Atkin Peter Swinnerton‐Dyer	17
+	Generalized Lambert series identities	2005	Song Heng Chan	14
+ PDF Chat	Dyson’s crank of a partition	1988	George E. Andrews Frank G. Garvan	13
+ PDF Chat	New combinatorial interpretations of Ramanujan’s partition congruences mod 5,7 and 11	1988	Frank G. Garvan	11
+	Rank and Conjugation for a Second Frobenius Representation of an Overpartition	2008	Jeremy Lovejoy	10
+	Ramanujan’s Notebooks: Part V	1997	Bruce C. Berndt	9
+ PDF Chat	M_2-rank differences for partitions without repeated odd parts	2009	Jeremy Lovejoy Robert Osburn	9
+	Rank and Conjugation for the Frobenius Representation of an Overpartition	2005	Jeremy Lovejoy	9
+	Higher order spt-functions	2011	Frank G. Garvan	8
+ PDF Chat	Overpartitions	2003	Sylvie Corteel Jeremy Lovejoy	8
+	The odd moments of ranks and cranks	2012	George E. Andrews Song Heng Chan Byungchan Kim	8
+ PDF Chat	The Ramanujan–Dyson identities and George Beck’s congruence conjectures	2020	George E. Andrews	8
+	Asymptotic inequalities for positive crank and rank moments	2013	Kathrin Bringmann Karl Mahlburg	8
+ PDF Chat	Asymptotics for rank and crank moments	2011	Kathrin Bringmann Karl Mahlburg Robert C. Rhoades	7
+ PDF Chat	Variations of Andrews-Beck type congruences	2020	Song Heng Chan Renrong Mao Robert Osburn	7
+	Ramanujan’s Notebooks	1991	Bruce C. Berndt	7
+	The Ranks and Cranks of Partitions Moduli 2, 3, and 4	2000	George Andrews Richard P. Lewis	6
+	On the total number of parts functions associated with ranks of partitions modulo 5 and 7	2021	Renrong Mao	6
+	The Theory of Partitions	1984	George E. Andrews	6
+	Some Observations on Dyson's New Symmetries of Partitions	2002	Alexander Bérkovich Frank G. Garvan	6
+ PDF Chat	Rank and crank moments for overpartitions	2009	Kathrin Bringmann Jeremy Lovejoy Robert Osburn	6
+	Cranks and dissections in Ramanujan's lost notebook	2004	Bruce C. Berndt Heng Huat Chan Song Heng Chan Wen-Chin Liaw	6
+	The generating functions of the rank and crank modulo 8	2007	Richard P. Lewis	6
+	Modular Functions and Dirichlet Series in Number Theory	1990	Tom M. Apostol	6
+ PDF Chat	On the Distribution of the spt-Crank	2013	George Andrews Freeman J. Dyson Robert C. Rhoades	5
+ PDF Chat	Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks	2007	George E. Andrews	5
+	Taylor coefficients of mock-Jacobi forms and moments of partition statistics	2014	Kathrin Bringmann Karl Mahlburg Robert C. Rhoades	5
+	On the Ranks of Partitions Modulo 9	1991	Richard P. Lewis	5
+	Mock Theta Functions	2002	Sander Zwegers	5
+ PDF Chat	On certain explicit congruences for mock theta functions	2010	Matthias Waldherr	5
+	None	2003	A. O. L. Atkin Frank G. Garvan	5
+	Relations Between the Rank and the Crank Modulo 9	1992	Richard P. Lewis	5
+	Inequalities between rank moments of overpartitions	2013	Renrong Mao	5
+ PDF Chat	Inequalities between ranks and cranks	2009	Kathrin Bringmann Karl Mahlburg	5
+ PDF Chat	M<sub>2</sub>-rank differences for overpartitions	2010	Jeremy Lovejoy Robert Osburn	5
+ PDF Chat	Relations Between the Ranks and Cranks of Partitions	2003	A. O. L. Atkin Frank G. Garvan	5
+	Proof of the Andrews–Dyson–Rhoades conjecture on the spt-crank	2014	William Y. C. Chen Kathy Q. Ji Wenston J. T. Zang	5
+	On Modular Forms of Half Integral Weight	1973	Goro Shimura	5
+	The number of smallest parts in the partitions of n	2008	George E. Andrews	5
+	Weighted partition rank and crank moments. III. A list of Andrews–Beck type congruences modulo 5, 7, 11 and 13	2021	Shane Chern	5
+ PDF Chat	Congruences for Ramanujan's φ function	2012	Song Heng Chan	5
+ PDF Chat	RANK DIFFERENCES FOR OVERPARTITIONS	2007	J. Lovejoy Robert Osburn	4
+ PDF Chat	The First Positive Rank and Crank Moments for Overpartitions	2016	George E. Andrews Song Heng Chan Byungchan Kim Robert Osburn	4
+	Ramanujan's Lost Notebook: Part II	2009	George E. Andrews Bruce C. Berndt	4
+	The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and 𝑞-series	2003	Ken Ono	4
+	ℓ-adic properties of smallest parts functions	2011	Scott Ahlgren Kathrin Bringmann Jeremy Lovejoy	4
+ PDF Chat	CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK	2010	Frank G. Garvan	4
+	On some relations between the rank and the crank	1992	Richard P. Lewis	4
+ PDF Chat	Inequalities for differences of Dyson’s rank for all odd moduli	2010	Kathrin Bringmann Ben Kane	4
+	Theta function identities and Ramanujan's Congruences on the partition function	2005	Wenchang Chu	4